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gg                       ANALYTICAL MECHANICS
and T, which are applied at the ends of the cord, and the reaction of the rough surface of C, with which if is in con-tact. It is desired to find the relaiion hehvecn '/' and T when the cord is just on the point of motion towards T(,
Fio. 44,
Consider the equilibrium of an element of thai part of the cord which is in contact with the surface*. Tho element is acted upon by the following throe forces:
The tensile force in the cord to the right of the element.
The tensile force in the cord to the loft of tin* element,
The reaction of the surface.
Let the tensile force to the left; of the element he denoted by T, then the tensile force to the right may he donotod hy T+dT. On the other hand if R denotes (ho reaction of the surface per unit length of the cord, the reaction on the element is R ds, where ds is the length of the element. We will, as usual, replace R by its Motional component F and its normal component NL